Chapter 18 gravitiational Fields Flashcards
What are properties of fields again
- what does everywhere property have
- what happens if the property with a field is put in the field of another
Anything with that type of property, be it charge or mass, will create a FIELD around it
If another thing with its own field is placed in this field, then there will be a FORCE exerted on both of the,
What is the key difference about the type of firce due to grav fields compared to other fields?
It is ALWAYS attractive, and thus two masses will always attract each other
What is equation for g, gravitational field stentgh?
The amount of Force felt due ti gravity/ per unit mass
G = F/m
If we work out force at surface, we see this is approximately 9.81
Gravity produces a RAIDAL field, what is this?
This is where the field lines start form a centre and move out,
And thus the closer th Enfield lines to each other the stronger thr field is felt
Badicsllt the field strength DECREASES a with distance away from the centre
What is a point mass and why can we model planets like one
Point mass is where all mass comc at one point.
Because the field lines are the same from both, and if we look at a planet from different ar away, it looks like a point mass
WE CAN MODEL BOTH AS POIMT MASSES, WITH RADIAL FIELDS EACH
How is a uniform field shown
Where do we see it
This is where all the field lines are PARALLEL TO EACH OTHER, and thus the grav field strentgh experienced is the SAME
This is basicallt what we see near to the surface of the earth
What is newtons law of gravitation for force
For a POINT MASS (thus model from the centre)
The force experienced by both masses are equal and act on each other
Force is DIRECTLY proportional the product of masses (Mm)
And inversely propritnsk to R2 (r distance between them)
Full equation for Force experienced by two masses
Why minus?
F = -GMm/r2
Where G is constant of proportionality and negative sign indicates it’s an ATTRACTIVE FORCE
As FORCE is a vector how ti find resultant force acting on amass that has a force due to different planets etc
If they’re at 90° the will have ti use pythag or angles
If horizontal, draw arrows and find the vector sum etc of them
How ti find gravitational field strength other equation in a radial field
(Experienced by a TEST mass at a distance r )
G= f/m, f = -GMm /r2
Then g = -GM/r2
So a point mass at a distance r will experience less g , and have less weight thus
What is g at infinity and 0 away
How will graph against r and 1/r2 look like
2)Why are graphs what you expect but just NEGATIVE?
At 0, g is infinity, at infinity, g is 0 (sun in)
Against r, it will look like 1/r2 graph, but minus
Against 1/r2, it will be proprtinal where gradient is -GM , so starts from 0
2) what you thought was correct for both graphs, however just flip in y axis because we are saying values for g start at max 0, and then get smaller thud negative and thus is bevause or NEGATIVE SIGN
- you are correvt, any proprtinsl MUST GO THROUGH 0, so either up or Down
Again why are g agsisnt r graphs negative etc
What is ti actually
Because if negative sign
It’s actually -g against r
Why is there a point between earth and moon where NET GRAV FIELD STRENGTH IS 0
2) so why is it closer to moon then earth
3) and why does it take more energy to send to moon then send to earth
Even at earth, our net grav field stenwtgj is field by earth - field by moon by vector addition
- problem is, it only we so far away but small mass, anyways this is negligible
As we go closer to moon, earth field decreases and moon field increases
THERE WILL BE SOME POIMT WHERE VECTOR ADDITION CANCELS THESE OUT
- then it increases again as the moons field is bigger than earth
2) it’s closer to moon then earth because earth mass so much bigger so at any distance the earth field will be bigger
- must be closer to the moon so earth field is less and can equal the moon
3) more of earth gravity must be overcome going this way compared to moons going the other way
Why is grav strentgh uniformish around surfsce?
Even if it decreases at factor r 2, the fact that the distance away from centre of earth is so small it’s negligible
Kepler 1st law of planetary motion
What does this means (eclipse, foci?)
Orbit of a planet is an ECLIPSE with the sun as one of its two foci
2) eclipses have two foci, and it’s sayifn all planets orbit forms shape of eclipse and the sun is at one of the two foci
However even though all planets orbit takes shape of eclipse, why can we MODEL IT AS A CIRCULAR ORBIT
this is because it has LOW ECCENTRICITY, which is a measure of how squashed (or how ecliptical ) the eclipse is
If it has low eccentricity it’d basically a circle
Okay 2nd law
A line segment connecting two positions of a planet orbit around the sun sweeps out the same area in the SAME AMOUMT OF TIME
Explain Kepler 2nd law
- fact it’s eclipse means what for postion of earth away from sun
- why does it travel faster closer to sun
Thus what does this mean for area
Basicallt as it’s an eclipse orbit, there will be some times where earth CLOSER to sun and times when further away
When it’s closer to the sun, the EARTH ORBITS FASTER DUE TO BEING CLOSER AND THUS HAVIGN GREATER GRAV FORCE (due to 1/x2)
And when it’s further away , it will orbit slower
However, as it’s further away, even a small radius travelled will equal the same area FROM THE SUN bevause it’s further away
Thus area of a line segment swept out by the earth will be the same in same time intervals bevause of the distances away increase when radius travels decrease .
Keplers third law
What does ti mean in essence, closer you are what
Modelling the orbit as circular, and thus circular motion takes place
Time period of orbit squared proportional to AVERAGE radius between earth and sun cubed
2) The closer you get to the centre , the less the time period is
How To derrive
Assume circular motion due to low eccentricity
- and then equate centripetal force to grav force
Rewrawnge and see t2 = 4pi2/GM r 3
So proprtinsl
And if drew graph would be straight line
What mass do you take to be big M
typically bigger mass
If you take sun mass, will find orbit of earth, if take earth, then kbit of sun
Basically mv2 /r is the thing that’s being ROTATED, this case the earth
BOTH PLANETS ORBIT EACH OTHER
Keplers laws only applet to sun earth?
No app,it’s ti anything orbiting each other
So satellites, moons etc
Why at any same radius, an object velocity of orbit will be the same
Through Keplers laws it shows you it only depends on the big mass
Why do satellites need to travel at a specific speed in order for them to actually orbit
2) however as the orbit isn’t acc a circle what do they normally have to be,p keep them in i rut)
3) but if we model them as circles, why DONT THEY NEED BOOSTERS
Based in equation and height above surfsce, they must travel at a certain speed so orbit can happened
2) normally have like boosters to accelerated and change speed when needed
But if modelled as circular orbit, once at right speed they don’t need boosters because no air resistance so constant velocity
How to make a geostationary orbit for a satellite and what conditions must be met
3 conditions
This is a satellite that stays in the SAME POSITION ABIBE EARTH at all times
- thus as earth orbits, it orbits in SYNC with it
- thus is must have an orbital period = to earth = 24 hours
2) must be above equator
3) must orbit same direction of earth
What will relative velocity of geostationary stalelites be
0
3 conditions for geo Sara let again
Why abibe equator?
Above equator
Time period 24 hours
Same orbit direction as earth
Bevause radius of earth constant probably , so height abibe earth always the same
How ti find the heigh all geostationary stalelites must be kept at
Sun in time period of 24 hours
USES OF SATELTIES
Main point, how do different satellites orbit differently to achieve these things
GPS
Reconnaissance (UAV)
Weather predictions , climate monitoring
Seicntific research
2) orbit closer to earth so time period less, further away, around poles etc
What is the definition of gravatiaonsk potential
This is the energy needed PER UNIT MASS, to take a point mass from INFINITY TO A POINT A DISTANCE AWAY FROM A MASS
How can you derrive equation
What is equation
Because energy = Fx d , we can use this
However as force varies with distance, must integrate from a point r away from mass to infinity, the forces
So integrating firce gives us equation for energy, -GMm/r
And as potential is the energy per unit MASS, must divide by point mass
Gives us potential = -GM/r
What is ptoentisl at infinity and what is it at r=0 pretty much
Why? What’s the thinking
What is max potential
When does potential increase decrease
So basically, as it’s attractive, moving the mass AWAY from point mass requires external ENERGY
And moving mass from infinity to POINT MASS is easy as it’s attractive, so actually RELEASES ENERGY
Think about potential as the amount of work needed to put in to take to Infinith
Thus closer to a point mass, or attraction, so more work needed to put in to separated, and thus more negative value
So as potential = -Gm/r
What is equation for (- otnetial , as potential take negative values ) against r
Lit just 1/r graph, where it approaches 0 at infinity because potential defined ti be 0 and max there
Going to moon , what happens to potential
Going away from point mass potential increases (less negaitive ) but approaches a moon so more nearby needed to put to separate so more negative
Reaches a maximum
Remember how to draw graph of proptinal ahsisnt r
Draw negative potential, getting closer to infinity potential increases going away from point mass closer to 0
How ti do scalar addition of potentials caused by multiple masses
Why will it approach 0 but never hit
Just add them separately tigether, bith will be negative will become more negative value
Bevause there will always be some potential
Why does falling down release energy whereas going up takes in
Look at change in potential
Falling down goes from less negative to more negative , so change is still negative, and thus energy released
Going up is more nergwitve to less so change positbe, energy required to separate
What is work done EQUATUIN
It is -GMm/ r
Basiclaly change in ptoentisl times energy
That’s why going firm low to high change in ptoentisl is positive so energy must be put in TO SEPARATE
What is escape velocity
The minimum amount vecoloty required ti give ti a body so that it can ESCPAE THE GRAVATAIONAL FIELD of another mass, without any FURTHER ENERGY INPUT (si in one go)
How does this happen
Why unrealistic
Must happen in ine go so non propelled
Escape is not necessarily infinity just for enough that potential is basicslly 0
And essentially all ke is transferred to gpe needed to “take it to infinity”
2) - never gonna be able to make an object go in one go
- also will always be resistance e
So how ti find how much v is needed ti properly something out if grav pull = infinity
Energy needed to take it to infinity at that point = -GMm/r
Energy transferred by kinetic = 1/2mv2
Equate and you’ll see min velocity is v = root 2GM/r
As a result, escape velocity the same for ALL MASSES
